Online shopping is gaining popularity. Traditional retailers with physical stores adjust to this trend by allowing their customers to shop online as well as offline, in-store. Increasingly, customers can browse and purchase products across multiple shopping channels. Understanding how customer behavior relates to the availability of multiple shopping channels is an important prerequisite for many downstream machine learning tasks, such as recommendation and purchase prediction. However, previous work in this domain is limited to analyzing single-channel behavior only. In this paper, we provide the first insights into multi-channel customer behavior in retail based on a large sample of 2.8 million transactions originating from 300,000 customers of a food retailer in Europe. Our analysis reveals significant differences in customer behavior across online and offline channels, for example with respect to the repeat ratio of item purchases and basket size. Based on these findings, we investigate the performance of a next basket recommendation model under multi-channel settings. We find that the recommendation performance differs significantly for customers based on their choice of shopping channel, which strongly indicates that future research on recommenders in this area should take into account the particular characteristics of multi-channel retail shopping.